Transmission system accuracy optimum allocation for multiaxis machine tools’ scheme design

Abstract

Transmission components are the main mechanical elements in a machine system, the accuracy level of the transmission system is one of the major sources of the machining error of multiaxis machine tools. This article investigates motion error analysis, volumetric motion error model for transmission system and the accuracy allocation method for multiaxis machine tools during the early design stage. For this purpose, a transmission system volumetric motion error model, which is based on the motion error matrix and screw theory, is derived for mapping transmission components' error parameters to the volumetric motion errors of machine tools. The volumetric motion error matrix combines motion errors along the machine tools' kinematic chains. Subsequently, the volumetric motion error model is expressed as a volumetric motion error twist, which is formulated from the volumetric motion error matrix. Additionally, the transmission system volumetric motion error twist model is used as design criteria for accuracy optimum allocation, with constraints on the twist magnitude and design variable limits. Then, design optimization is performed by using a multiobjective nonlinear optimization technique to minimize the manufacturing cost and volumetric motion error twist pitch. To solve this multiple objective optimum problem, this study proposes an approach integrating Lagrange multiplier and gradient descent operator with non-dominated sorting genetic algorithm-II (NSGA-II). Modified non-dominated sorting genetic algorithm-II searches for an allocation scheme Pareto optimal front. Consequently, VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) determines the best compromise solution from the Pareto set. Finally, a numerical experiment for the optimal design of a numerical control machine tool is conducted, which highlights the advantages of the proposed methodology.

A new geometric error budget method of multi-axis machine tool based on improved value analysis

“…On the basis of satisfying support and credibility, the rough chain set theory is used to reduce the rules and improve the accuracy and rationality of computer-aided tolerance design decision. Cheng et al 46 proposed a novel robust accuracy allocation method for multi-axis machine tools based on multiobjective quality and cost trade-offs. The proposed method can realize the optimization of geometric accuracy and can determine the optimal accuracy grade of the feeding components satisfying the machining accuracy requirements.…”

“…Cheng et al. 46 proposed a novel robust accuracy allocation method for multi-axis machine tools based on multi-objective quality and cost trade-offs. The proposed method can realize the optimization of geometric accuracy and can determine the optimal accuracy grade of the feeding components satisfying the machining accuracy requirements.…”

Analysis and Compensation for Gear Accuracy with Setting Error in Form Grinding

“…Gear setting error is a common static geometric error in the process of form grinding. Some classic error modeling techniques for machine tools such as homogeneous transformation matrix (HTM), Denavit-Hartenberg (D-H) method, rigid body kinematics, and screw theory were reported in previous research works [1][2][3]. Park et al [4] discussed a HTM method for geometric errors of a rotary axis of miniaturized five-axis machine tools, which developed the research foundation of this paper.…”

A new method for motion accuracy allocation of mechanical transmission system based on interval intuitionistic trapezoidal fuzzy number and Meta-action theory

“…Using the above methods, the error of mechanical transmission system can be analyzed and visually described [20]. However, the above error analysis methods have obvious deficiencies in the process of motion error modeling and analysis.…”

“…During the research of accuracy optimal allocation of mechanical system, the objective function in the allocation model are usually the comprehensive manufacturing cost and the quality loss [20,23]. Scholars further analyzed the influencing factors of manufacturing cost and correct the manufacturing cost to make the analysis results conform to the engineering practice.…”